Exercise 59

The expression ( (x + b)^{-2} div (x + b)^{-5} )   equals: ( (x + b)^{-3} ) ( (x + b) ) ( (x + b)^3 ) ( (x + b)^{-7} ) ( (x + b)^7 ) Try to solve it before checking the answer. Answer ( (x + b)^3 ) Step by Step […]

Exercise 60

In a circle with radius ( r ), ( frac{1}{ pi} ) times the circumference is: twice the diameter the radius the semi circumference the diameter half the radius Try to solve it before checking the answer. Answer the diameter Step by Step Solution The length of the circumference is ( 2pi r ). Hence: […]

Exercise 58

The figure shows a quadrilateral ( ABCD ) inscribed in a circle. ( overline{AC} ) is a diameter, ( overline{AB} = 40 , cm ) and ( overline{BC} = 30 , cm ). What is the area of the shaded region? ( 1250 pi – 600 ) ( cm^2 ) ( 2500 pi ) ( […]

Exercise 57

When solving the system   ( begin{cases} 2x + y = 50 \ 4x – 5y = 30 end{cases} )   we obtain that ( 5(x + y) ) equals: 50 100 200 150 300 Try to solve it before checking the answer. Answer 150 Step by Step Solution Multiplying the first equation by -2 […]

Exercise 56

An affine function ( y = y(x) ) takes the value ( 81.5 ) when ( x = 13 ), and the value ( 96.7 ) when ( x = 20.6 ). What is the correspondence rule? ( y = 0.5x + 75 ) ( y = 2x + 55.5 ) ( y = 0.5x […]

Exercise 55

We have the geometric progression (x), (y), (z). We know that (x) is different from (y), that (y) is not zero, and that (x), (2y), (3z) form an arithmetic progression. The ratio of the geometric progression is: ( frac{4}{3} ) ( 1 ) ( frac{1}{3} ) ( 2 ) ( frac{2}{3} ) Try to solve […]

Exercise 54

The set of points on the real number line whose distances to point 3 are smaller than their distances to point 5 is: ( -infty , , 3 ) ( (4 , +infty) ) ( (4 , , 5) ) ( (-infty , , 4) cap (5, +infty) ) ( (-infty , , 4) ) […]

Exercise 53

If ( cfrac{2(1 – t) + 5t}{ 4 } = 1 ), then ( cfrac{t^2 – t}{ 3 } ) equals: ( frac{2}{3} ) ( – frac{2}{27} ) ( frac{1}{9} ) ( – frac{6}{27} ) (- frac{2}{9} ) Try to solve it before checking the answer. Answer ( – frac{2}{27} ) Step by Step Solution […]

Exercise 52

The triangles ( triangle ABC ) and ( triangle PBQ ) in the figure are similar triangles. Moreover, the value of the ratio ( frac{ overline{PB} }{ overline{ AB}} ) is ( frac{2}{3} ). What is the value of ( x )? ( frac{1}{4} ) ( frac{2}{3} ) ( 3 ) (4) ( frac{3}{2} ) […]

Exercise 51

If the numbers 61, 59, 56, 52, (z), (y), (x), were generated following a specific pattern of regularity, what is the value of (x)? 47 34 31 33 35 Try to solve it before checking the answer. Answer 34 Step by Step Solution If we subtract its successor from each number, we get: This diagram […]